The correlation between magnetic properties and microscopic structural aspects in the diluted magnetic semiconductor Ge$_{1-x}$Mn$_{x}$Te is investigated by x-ray diffraction and magnetization as a function of the Mn concentration $x$. The occurrence of high ferromagnetic-transition temperatures in the rhombohedrally distorted phase of slowly-cooled Ge$_{1-x}$Mn$_{x}$Te is shown to be directly correlated with the formation and coexistence of strongly-distorted Mn-poor and weakly-distorted Mn-rich regions. It is demonstrated that the weakly-distorted phase fraction is responsible for the occurrence of high-transition temperatures in Ge$_{1-x}$Mn$_{x}$Te. When the Mn concentration becomes larger, the Mn-rich regions start to switch into the undistorted cubic structure, and the transition temperature is suppressed concurrently. By identifying suitable annealing conditions, we successfully increased the transition temperature to above 200 K for Mn concentrations close to the cubic phase. Structural data indicate that the weakly-distorted phase fraction can be restored at the expense of the cubic regions upon the enhancement of the transition temperature, clearly establishing the direct link between high-transition temperatures and the weakly-distorted Mn-rich phase fraction.
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